Adding It All Up

"In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles." Along with the Angle Sum tool provided, this lesson demonstrates the relationship between a polygon's number of sides and the polygon's sum of interior (180(n-2)) angles using triangulation and prompts for students to conceive and validate the pattern through experimentation.

Standards & Objectives

Academic standards
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right...
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
GLE 0806.4.5
Use visualization to describe or identify intersections, cross-sections, and various views of geometric figures.
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
Learning objectives: 

Learning Objectives:

Students will:

  • Investigate the pattern between the number of sides of a polygon and the sum of the interior angles using in two different methods.
  • Determine that the interior angle sum is always the same for polygons with the same number of sides.
  • Create a formula to find the interior angle sum given the number of sides.
  • Explore interior angles in regular polygons.
Essential and guiding questions: 

Questions for Students:

  • Are all the angle measures always the same for a single polygon
  • As the number of sides increases, what happens to the sum of the angle measures? 
  • Does the formula work for both regular and non-regular polygons? What about shapes like scalene triangles or trapezoids?

Lesson Variations

Blooms taxonomy level: 
Extension suggestions: 


  • Have students explore exterior angles. The sum of the exterior angles for any polygon is 360°, and therefore the measure of one exterior angle in a regular polygon is 360/n 
  • In the bottom right-hand corner of the Angle Sum Tool, there is an animation for the triangle and square showing how the sum of the interior angles relates to tiling. Have students watch the animations and write a journal entry on what they demonstrate.


Helpful Hints


  • Computers with internet access
  • Adding It All Up Activity Sheet 
  • Adding It All Up Answer Key 
  • Unlined paper
  • Rulers
  • Colored pencils or markers (optional)
  • Computers with Internet access